On-line data-driven control for uncertain systems based on greedy algorithm

Abstract

Considering a result that persistently exciting data can be used to replace the linear system model, this paper is devoted to applying this result in the field of data-driven control of nonlinear systems. An on-line iteration based on greedy algorithm to stabilize uncertain discrete-time systems is proposed. The method tends to obtain approximate optimal control through solving a series of programming problems. Every programming problem is linear for the convenience of solving. Besides, in particular, the method requires few prior conditions, as long as the system is controllable and observable and the equilibrium state of the system is known. First, we prove that under certain circumstances, the solution to our linear matrix inequality can stabilize the system. Next, a multi-objective programming problem is proposed to deal with situations where the required conditions are unknown. Finally, an on-line iteration is used to enhance robustness as well as real-time evaluation. The method is illustrated to be effective through a simulation under repeated experiments.